The use of antireflection layers (or “λ/4” layers) to increase the optical contrast of an object observed by reflection optical microscopy is a very powerful technique that has been known for many years; in particular, it allowed the first observation of molecular walks by Langmuir and Blodgett in 1937 and, more recently, the viewing of graphene layers by Novoselov et al.
Let I be the luminous intensity reflected by the object to be observed, deposited on a support, and Is that reflected by the support alone; then, the contrast with which the sample is observed equals C=(I−Is)/(I+Is). It is understood that the absolute value of this contrast takes its maximum value (equal to 1) when Is=0, that is to say when the support has zero reflectivity, or else when the supported object has zero reflectivity. In the simplest case, the condition Is=0 is satisfied by using in the guise of support a transparent substrate on which is deposited a thin layer, likewise transparent, whose thickness and refractive index are chosen in an opportune manner. In the case of a single antireflection layer, illuminated under normal incidence with a transparent and semi-infinite incident medium (from which the illumination originates) and a transparent and semi-infinite emergent medium (the substrate), the following conditions are obtained:n12=n0n3  (1a)n1e1=λ/4  (1b)where n1 is the refractive index (real) of the layer, n0 and n3 the refractive indices (also real) of the incident and emergent media, e1 the thickness of the layer and λ the illumination wavelength.
For given incident and emergent media, equation (1a) determines in a one-to-one manner the refractive index of the antireflection layer. Unfortunately, this index might not correspond to a commonly used material or one which satisfies diverse constraints related to the application specifically considered. For example, in the case of an air-glass interface—the practical interest of which is obvious—we obtain n1≅1.27, thus requiring the use of composite materials such as aerogels.